Robustness of network coherence in asymmetric unicyclic graphs

In this paper, we propose a family of unicyclic graphs to study robustness of network coherence quantified by the Laplacian spectrum, which measures the extent of consensus under the noise. We adjust the network parameters to change the structural asymmetries with an aim of studying their effects on the coherence. Using the graph’s structures and matrix theories, we obtain closed-form solutions of the network coherence regarding network parameters and network size. We further show that the coherence of the asymmetric graph is higher than the corresponding symmetric graph and also compare the consensus behaviors for the graphs with different asymmetric structures. It displays that the coherence of the unicyclic graph with one hub is better than the graph with two hubs. Finally, we investigate the effect of degree of hub nodes on the coherence and find that bigger difference of degrees leads to better coherence.

Leontief Meets Markov: Sectoral Vulnerabilities Through Circular Connectivity

Economists have been aware of the mapping between an Input-Output (I-O, hereinafter) table and the adjacency matrix of a weighted digraph for several decades (Solow, Econometrica 20(1):29–46, 1952). An I-O table may be interpreted as a network in which edges measure money flows to purchase inputs that go into production, whilst vertices represent economic industries. However, only recently the language and concepts of complex networks (Newman 2010) have been more intensively applied to the study of interindustry relations (McNerney et al. Physica A Stat Mech Appl, 392(24):6427–6441, 2013). The aim of this paper is to study sectoral vulnerabilities in I-O networks, by connecting the formal structure of a closed I-O model (Leontief, Rev Econ Stat, 19(3):109–132, 1937) to the constituent elements of an ergodic, regular Markov chain (Kemeny and Snell 1976) and its chance process specification as a random walk on a graph. We provide an economic interpretation to a local, sector-specific vulnerability index based on mean first passage times, computed by means of the Moore-Penrose inverse of the asymmetric graph Laplacian (Boley et al. Linear Algebra Appl, 435(2):224–242, 2011). Traversing from the most central to the most peripheral sector of the economy in 60 countries between 2005 and 2015, we uncover cross-country salient roles for certain industries, pervasive features of structural change and (dis)similarities between national economies, in terms of their sectoral vulnerabilities.

Probability Ordinal-Preserving Semantic Hashing for Large-Scale Image Retrieval

Semantic hashing enables computation and memory-efficient image retrieval through learning similarity-preserving binary representations. Most existing hashing methods mainly focus on preserving the piecewise class information or pairwise correlations of samples into the learned binary codes while failing to capture the mutual triplet-level ordinal structure in similarity preservation. In this article, we propose a novel Probability Ordinal-preserving Semantic Hashing (POSH) framework, which for the first time defines the ordinal-preserving hashing concept under a non-parametric Bayesian theory. Specifically, we derive the whole learning framework of the ordinal similarity-preserving hashing based on the maximum posteriori estimation, where the probabilistic ordinal similarity preservation, probabilistic quantization function, and probabilistic semantic-preserving function are jointly considered into one unified learning framework. In particular, the proposed triplet-ordering correlation preservation scheme can effectively improve the interpretation of the learned hash codes under an economical anchor-induced asymmetric graph learning model. Moreover, the sparsity-guided selective quantization function is designed to minimize the loss of space transformation, and the regressive semantic function is explored to promote the flexibility of the formulated semantics in hash code learning. The final joint learning objective is formulated to concurrently preserve the ordinal locality of original data and explore potentials of semantics for producing discriminative hash codes. Importantly, an efficient alternating optimization algorithm with the strictly proof convergence guarantee is developed to solve the resulting objective problem. Extensive experiments on several large-scale datasets validate the superiority of the proposed method against state-of-the-art hashing-based retrieval methods.

Towards Optimal Discrete Online Hashing with Balanced Similarity

When facing large-scale image datasets, online hashing serves as a promising solution for online retrieval and prediction tasks. It encodes the online streaming data into compact binary codes, and simultaneously updates the hash functions to renew codes of the existing dataset. To this end, the existing methods update hash functions solely based on the new data batch, without investigating the correlation between such new data and the existing dataset. In addition, existing works update the hash functions using a relaxation process in its corresponding approximated continuous space. And it remains as an open problem to directly apply discrete optimizations in online hashing. In this paper, we propose a novel supervised online hashing method, termed Balanced Similarity for Online Discrete Hashing (BSODH), to solve the above problems in a unified framework. BSODH employs a well-designed hashing algorithm to preserve the similarity between the streaming data and the existing dataset via an asymmetric graph regularization. We further identify the “data-imbalance” problem brought by the constructed asymmetric graph, which restricts the application of discrete optimization in our problem. Therefore, a novel balanced similarity is further proposed, which uses two equilibrium factors to balance the similar and dissimilar weights and eventually enables the usage of discrete optimizations. Extensive experiments conducted on three widely-used benchmarks demonstrate the advantages of the proposed method over the stateof-the-art methods.